Some special families of holomorphic and Sălăgean type bi-univalent functions associated with Horadam polynomials involving a modified sigmoid activation function

Year 2021, Volume: 50 Issue: 3, 710 - 720, 07.06.2021

S R Swamy , Serap Bulut , Sailaja Yerragunta

https://doi.org/10.15672/hujms.695858

Cited By: 18

Abstract

The aim of this paper is to introduce some special families of holomorphic and S\u{a}l\u{a}gean type bi-univalent functions by making use of Horadam polynomials involving the modified sigmoid activation function $\phi(s)=\frac{2}{1+e^{-s} },\,s\geq0$ in the open unit disc $\mathfrak{D}$. We investigate the upper bounds on initial coefficients for functions of the form $g_{\phi}(z)=z+\sum\limits_{j=2}^{\infty}\phi(s)d_jz^j$, in these newly introduced special families and also discuss the Fekete-Szegö problem. Some interesting consequences of the results established here are also indicated.

Keywords

Holomorphic function, Bi-univalent function, Fekete - Szegö inequality, Horadam polynomials, modified sigmoid function

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